login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A207625 Triangle of coefficients of polynomials u(n,x) jointly generated with A207626; see the Formula section. 4
1, 2, 4, 3, 7, 12, 3, 11, 32, 21, 3, 16, 70, 83, 30, 3, 22, 135, 247, 161, 39, 3, 29, 238, 616, 622, 266, 48, 3, 37, 392, 1358, 1946, 1276, 398, 57, 3, 46, 612, 2730, 5244, 4854, 2290, 557, 66, 3, 56, 915, 5106, 12630, 15622, 10312, 3745, 743, 75, 3, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..57.

FORMULA

u(n,x)=u(n-1,x)+v(n-1,x),

v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2

4....3

7....12...3

11...32...21...3

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + v[n - 1, x]

v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1

Table[Factor[u[n, x]], {n, 1, z}]

Table[Factor[v[n, x]], {n, 1, z}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A207625 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A207626 *)

CROSSREFS

Cf. A207626.

Sequence in context: A223625 A166017 A257504 * A238953 A238964 A035507

Adjacent sequences:  A207622 A207623 A207624 * A207626 A207627 A207628

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling, Feb 21 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 19:24 EDT 2019. Contains 328127 sequences. (Running on oeis4.)